question_answer

If \[A=\frac{3}{\sqrt{3}}+1+\frac{1}{\sqrt{3}}+\frac{1}{3}+.....\infty \] then find the value of \[A-\frac{1}{A}\].

A)  \[\frac{3\,\sqrt{3}-1}{6}\]                     

B)  \[\frac{7\sqrt{3}+11}{6}\] 

C)  \[\frac{3\,\sqrt{3}\,+1}{6}\]                  

D)  \[\frac{7\,\sqrt{3}-11}{6}\]

E)  None of these